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This morning my co-worker asked me if I wanted some coffee. I said, "No thanks, I can't drink coffee because it upsets my stomach." I was thinking of how I'd say this in Japanese, but I'm not sure which is the most appropriate way to say "can't" in this situation.

It seems like saying 飲めない or 飲むことができない would only be correct if I physically couldn't get the coffee down my throat. Since that's not the case and I'm using "can't" to really mean "I won't because of the undesirable after effects", those two seem wrong.

Is either of コーヒーを・は飲み得ない, 飲むわけにはいかない more correct and/or preferrable? Or would something without potential, like 飲みにくい・づらい・がたい work better?

Update: I knew I was forgetting an option when I wrote this topic. I left out the possibility of 飲みかねる, but that sounds really wrong to me.

I think ～かねる/～かねます sounds literary and formal, is more used in business situations, towards customers/clients, than in casual/daily communication, often in an instruction manual or a warranty, eg...「返品/キャンセルはお受け致しかねます。/お受けしかねます。」
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user1016May 23 '13 at 16:29

Unfortunately, 〜飲み得ない might be better used in poetry rather than everyday conversation.

And 〜飲むわけにはいかない or 〜飲むわけにはいけない might rather be used more for when something is just "undrinkable" (perhaps something not potable) instead of something you personally cannot (or possibly don't like to) drink.

At any rate, along with @Chocolate's point about「〜飲めないんです。」 another possible option (depending on your audience) could be something simple like: 「私はコーヒーがだめです。」 (And some of those particles can even be dropped...)

@istrasci Thanks for the clarification. I guess my main point about "simplicity" in regard to the Japanese language is the idea that there will often be cases where we can't directly convert our native language understanding to another language (such as Japanese) :) Even when grammar is correct (or at least theoretically correct,) the usage might still (unfortunately) be formed from our native language understanding... instead of thinking from the perspective of the other language (i.e. thinking in Japanese.)
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summeaMay 15 '13 at 19:29

I would say,"コーヒーは飲めないんです” I think only this sentence works. It's like "お酒はのめないんです。”This sentence implies that you cannot drink it because it affects your stomach or maybe you're allergic to that. But if that person asks why, I would say,"お腹が痛くなります".or ”気持ちが悪くなります。” If it seriously affects your stomach, I would say, ”体が受け付けません” It means that my body doesn't accept it.